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## What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

- The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
- The equations section lets you solve an equation or system of equations. You can usually find the exact answer or, if necessary, a numerical answer to almost any accuracy you require.
- The inequalities section lets you solve an inequality or a system of inequalities for a single variable. You can also plot inequalities in two variables.
- The calculus section will carry out differentiation as well as definite and indefinite integration.
- The matrices section contains commands for the arithmetic manipulation of matrices.
- The graphs section contains commands for plotting equations and inequalities.
- The numbers section has a percentages command for explaining the most common types of percentage problems and a section for dealing with scientific notation.

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## Free Math Worksheets — Over 100k free practice problems on Khan Academy

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## Statistics and probability

High school statistics, ap®︎/college statistics, precalculus, differential calculus, integral calculus, ap®︎/college calculus ab, ap®︎/college calculus bc, multivariable calculus, differential equations, linear algebra.

- Addition and subtraction
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- Intro to multiplication
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- Add decimals
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- Multi-digit multiplication and division
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## Frequently Asked Questions about Khan Academy and Math Worksheets

Why is khan academy even better than traditional math worksheets.

Khan Academy’s 100,000+ free practice questions give instant feedback, don’t need to be graded, and don’t require a printer.

## What do Khan Academy’s interactive math worksheets look like?

Here’s an example:

## What are teachers saying about Khan Academy’s interactive math worksheets?

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## Unit 2: Solving equations & inequalities

About this unit, linear equations with variables on both sides.

- Why we do the same thing to both sides: Variable on both sides (Opens a modal)
- Intro to equations with variables on both sides (Opens a modal)
- Equations with variables on both sides: 20-7x=6x-6 (Opens a modal)
- Equation with variables on both sides: fractions (Opens a modal)
- Equation with the variable in the denominator (Opens a modal)
- Equations with variables on both sides Get 3 of 4 questions to level up!
- Equations with variables on both sides: decimals & fractions Get 3 of 4 questions to level up!

## Linear equations with parentheses

- Equations with parentheses (Opens a modal)
- Reasoning with linear equations (Opens a modal)
- Multi-step equations review (Opens a modal)
- Equations with parentheses Get 3 of 4 questions to level up!
- Equations with parentheses: decimals & fractions Get 3 of 4 questions to level up!
- Reasoning with linear equations Get 3 of 4 questions to level up!

## Analyzing the number of solutions to linear equations

- Number of solutions to equations (Opens a modal)
- Worked example: number of solutions to equations (Opens a modal)
- Creating an equation with no solutions (Opens a modal)
- Creating an equation with infinitely many solutions (Opens a modal)
- Number of solutions to equations Get 3 of 4 questions to level up!
- Number of solutions to equations challenge Get 3 of 4 questions to level up!

## Linear equations with unknown coefficients

- Linear equations with unknown coefficients (Opens a modal)
- Why is algebra important to learn? (Opens a modal)
- Linear equations with unknown coefficients Get 3 of 4 questions to level up!

## Multi-step inequalities

- Inequalities with variables on both sides (Opens a modal)
- Inequalities with variables on both sides (with parentheses) (Opens a modal)
- Multi-step inequalities (Opens a modal)
- Using inequalities to solve problems (Opens a modal)
- Multi-step linear inequalities Get 3 of 4 questions to level up!
- Using inequalities to solve problems Get 3 of 4 questions to level up!

## Compound inequalities

- Compound inequalities: OR (Opens a modal)
- Compound inequalities: AND (Opens a modal)
- A compound inequality with no solution (Opens a modal)
- Double inequalities (Opens a modal)
- Compound inequalities examples (Opens a modal)
- Compound inequalities review (Opens a modal)
- Solving equations & inequalities: FAQ (Opens a modal)
- Compound inequalities Get 3 of 4 questions to level up!

Examples for

## Mathematics

Wolfram|Alpha has broad knowledge and deep computational power when it comes to math. Whether it be arithmetic, algebra, calculus, differential equations or anything in between, Wolfram|Alpha is up to the challenge. Get help with math homework, solve specific math problems or find information on mathematical subjects and topics.

Do basic arithmetic. Work with fractions, percentages and similar fundamentals. Solve place value and word problems.

## Do basic arithmetic:

Do exact arithmetic with fractions:.

Compute the properties of geometric objects of various kinds in 2, 3 or higher dimensions. Explore and apply ideas from many subfields of geometry.

## Compute properties of a geometric figure:

Plot a conic section and identify its type:, compute properties of a polyhedron:.

Work with various kinds of numbers. Check for membership in larger sets, such as the rationals or the transcendental numbers. Convert between bases.

## Compute a decimal approximation to a specified number of digits:

Convert a decimal number to another base:.

Analyze integers; subsets of the integers, including the prime numbers; and related ideas.

## Compute a prime factorization:

Solve a diophantine equation:.

Perform numerical analysis and optimization of systems and objects, including packing and covering of objects and control systems.

## Minimize or maximize a function:

Numerically integrate functions that cannot be integrated symbolically:.

Make queries about various definitions and descriptions in mathematics.

## Find information about a math concept:

Get a brief definition:.

Compute properties of datasets, perform statistical inference or model data. Work with probability distributions and random variables.

## Calculate basic descriptive statistics for a data set:

Find the sample size needed to estimate a binomial parameter:.

Find roots of and expand, factor or simplify mathematical expressions—everything from polynomials to fields and groups.

## Solve an equation:

Factor a polynomial:, simplify an expression:.

Solve differential equations of any order. Examine solutions and plots of the solution families. Specify initial conditions to find exact solutions.

## Solve a linear ordinary differential equation:

Specify initial values:, solve a nonlinear equation:.

Perform trigonometric calculations and explore properties of trigonometric functions and identities.

## Compute values of trigonometric functions:

Solve a trigonometric equation:.

Explore sequences and recurrences, solve common problems in combinatorics and compute properties of graphs and lattices.

## Compute a possible formula and continuation for a sequence:

Analyze a graph specified by adjacency rules:, solve a recurrence:.

Evaluate Boolean logic expressions and expressions involving sets and set operators. Solve Boolean equations. Compute truth tables. Generate Venn diagrams.

## Compute a truth table:

Generate a venn diagram:.

Gather information about famous problems, conjectures, theorems and paradoxes. Learn about them and their formulators.

## Get information about a mathematical conjecture:

Get historical information about a theorem:.

Compute the probabilities of certain events occurring. Compute joint, disjoint or conditional probabilities and apply them to real-world situations.

## Compute the probability of a union of events:

Compute coin‐toss probabilities:.

Compute integrals, derivatives and limits as well as analyze sums, products and series.

## Compute an integral:

Calculate a derivative:, solve an ordinary differential equation:.

Visualize functions, equations and inequalities. Do so in 1, 2 or 3 dimensions. Make polar and parametric plots.

## Plot a function:

Plot a region satisfying multiple inequalities:.

Explore and compute properties of vectors, matrices and vector spaces.

## Compute properties of a vector:

Calculate properties of a matrix:, determine whether a set of vectors is linearly independent:.

Analyze functions and expressions containing imaginary numbers or complex variables.

## Compute properties of a function of a complex variable (use the variable z ):

Compute the residue of a function at a point:.

Examine the properties of mathematical functions, such as continuity, surjectivity and parity. Utilize notable special functions or number theoretic functions.

## Do computations with special functions:

Do computations with number theoretic functions:, find representations for a function:.

Compute; learn about algorithms, definitions and theorems involving; or find properties of continued fractions.

## Find the continued fraction representation of a number:

Find definitions of continued fraction terminology:, find continued fraction papers by author:.

Get information about math Common Core Standards for kindergarten through eighth grade.

## Evaluate an expression (CCSS.Math.Content.6.EE.A.2c):

Perform multiple operations with rational numbers (ccss.math.content.7.ns.a.2c):.

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- AA Similarity
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- Greatest Common Factors (GCFs)
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- Power of a Power Property
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- Power Series and Radius of Convergence
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Word Problem: Rachel has 17 apples. She gives some to Sarah. Sarah now has 8 apples. How many apples did Rachel give her?

Simplified Equation: 17 - x = 8

Word Problem: Rhonda has 12 marbles more than Douglas. Douglas has 6 marbles more than Bertha. Rhonda has twice as many marbles as Bertha has. How many marbles does Douglas have?

Variables: Rhonda's marbles is represented by (r), Douglas' marbles is represented by (d) and Bertha's marbles is represented by (b)

Simplified Equation: {r = d + 12, d = b + 6, r = 2 × b}

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1. Mrs. Rodger got a weekly raise of $145. If she gets paid every other week, write an integer describing how the raise will affect her paycheck.

Let the 1st paycheck be x (integer). Mrs. Rodger got a weekly raise of $ 145. So after completing the 1st week she will get $ (x+145). Similarly after completing the 2nd week she will get $ (x + 145) + $ 145. = $ (x + 145 + 145) = $ (x + 290) So in this way end of every week her salary will increase by $ 145.

3. Mr. Jones sold two pipes at $1.20 each. Based on the cost, his profit one was 20% and his loss on the other was 20%. On the sale of the pipes, he: (a) broke even, (b) lost 4 cents, (c) gained 4 cents, (d) lost 10 cents, (e) gained 10 cents Solution:

Selling price of the first pipe = $1.20

Profit = 20%

Let’s try to find the cost price of the first pipe

CP = Selling price - Profit

CP = 1.20 - 20% of CP

CP = 1.20 - 0.20CP

CP + 0.20CP = 1.20

1.20CP = 1.20

CP = \(\frac{1.20}{1.20}\)

Selling price of the Second pipe = $1.20

Let’s try to find the cost price of the second pipe

CP = Selling price + Loss

CP = 1.20 + 20% of CP

CP = 1.20 + 0.20CP

CP - 0.20CP = 1.20

0.80CP = 1.20

CP = \(\frac{1.20}{0.80}\)

Therefore, total cost price of the two pipes = $1.00 + $1.50 = $2.50

And total selling price of the two pipes = $1.20 + $1.20 = $2.40

Loss = $2.50 – $2.40 = $0.10

Therefore, Mr. Jones loss 10 cents.

Answer: (d)

5. A man has $ 10,000 to invest. He invests $ 4000 at 5 % and $ 3500 at 4 %. In order to have a yearly income of $ 500, he must invest the remainder at: (a) 6 % , (b) 6.1 %, (c) 6.2 %, (d) 6.3 %, (e) 6.4 % Solution: Income from $ 4000 at 5 % in one year = $ 4000 of 5 %. = $ 4000 × 5/100. = $ 4000 × 0.05. = $ 200. Income from $ 3500 at 4 % in one year = $ 3500 of 4 %. = $ 3500 × 4/100. = $ 3500 × 0.04. = $ 140. Total income from 4000 at 5 % and 3500 at 4 % = $ 200 + $ 140 = $ 340. Remaining income amount in order to have a yearly income of $ 500 = $ 500 - $ 340. = $ 160. Total invested amount = $ 4000 + $ 3500 = $7500. Remaining invest amount = $ 10000 - $ 7500 = $ 2500. We know that, Interest = Principal × Rate × Time Interest = $ 160, Principal = $ 2500, Rate = r [we need to find the value of r], Time = 1 year. 160 = 2500 × r × 1. 160 = 2500r 160/2500 = 2500r/2500 [divide both sides by 2500] 0.064 = r r = 0.064 Change it to a percent by moving the decimal to the right two places r = 6.4 % Therefore, he invested the remaining amount $ 2500 at 6.4 % in order to get $ 500 income every year. Answer: (e) 6. Jones covered a distance of 50 miles on his first trip. On a later trip he traveled 300 miles while going three times as fast. His new time compared with the old time was: (a) three times as much, (b) twice as much, (c) the same, (d) half as much, (e) a third as much Solution: Let speed of the 1st trip x miles / hr. and speed of the 2nd trip 3x / hr. We know that Speed = Distance/Time. Or, Time = Distance/Speed. So, times taken to covered a distance of 50 miles on his first trip = 50/x hr. And times taken to covered a distance of 300 miles on his later trip = 300/3x hr. = 100/x hr. So we can clearly see that his new time compared with the old time was: twice as much. Answer: (b)

11. Kalin walks at a constant rate of 5/8 kilometers per hour. The beach is 3/4 kilometers from his home. How long does it take Kalin to walk from his home to the beach?

Speed = \(\frac{5}{8}\) kilometers per hour.

Distance = \(\frac{3}{4}\) kilometers

Distance = Speed × Time

or, Time = Distance/Speed

= (\(\frac{3}{4}\) ÷ \(\frac{5}{8}\)) hours

= (\(\frac{3}{4}\) × \(\frac{8}{5}\)) hours

= \(\frac{24}{20}\) hours

= \(\frac{6}{5}\) hours

= 1\(\frac{1}{5}\) hours

Answer: 1\(\frac{1}{5}\) hours

Unsolved Questions:

1. Fahrenheit temperature F is a linear function of Celsius temperature C. The ordered pair (0, 32) is an ordered pair of this function because 0°C is equivalent to 32°F, the freezing point of water. The ordered pair (100, 212) is also an ordered pair of this function because 100°C is equivalent to 212° F, the boiling point of water.

2. A sports field is 300 feet long. Write a formula that gives the length of x sports fields in feet. Then use this formula to determine the number of sports fields in 720 feet.

3. A recipe calls for 2 1/2 cups and I want to make 1 1/2 recipes. How many cups do I need?

4. Mario answered 30% of the questions correctly. The test contained a total of 80 questions. How many questions did Mario answer correctly?

5. Mary’s credit card company charges 16% interest on her outstanding credit card balance each month. Her minimum payment is $20 each month. Mary’s credit card bill is $70 in January. Mary only pays the minimum amount each month, and she does not spend any additional money on her credit card. How long, in months, will it take her to pay off her bill from January?

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## Preprocessing when solving generalized eigenvalue problems using the eigs function

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- Start off using Anew = inv(R)*A*inv(R)', with B = R'*R
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## Solving a quadratic optimization problem subjected to linear constraints

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## quadprog is too slow for a convex unconstrained quadratic problem

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https://www.mathworks.com/matlabcentral/answers/2048462-quadprog-is-too-slow-for-a-convex-unconstrained-quadratic-problem

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## Accepted Answer

## Direct link to this answer

https://www.mathworks.com/matlabcentral/answers/2048462-quadprog-is-too-slow-for-a-convex-unconstrained-quadratic-problem#answer_1360437

- Conjugate Gradient Method : This is an iterative method specifically designed for solving large systems of linear equations or large-scale unconstrained optimization problems, particularly when the matrix ( A ) is symmetric positive semidefinite. MATLAB's built-in ' pcg' (Preconditioned Conjugate Gradient) function can be used for this purpose. Refer to the following MathWorks documentation for detailed information about 'pcg' function: https://www.mathworks.com/help/matlab/ref/pcg.html
- LSQR: The LSQR algorithm is an iterative method for solving large-scale linear systems and least-squares problems. Although it's not specifically designed for quadratic programming, it can be effective for large and sparse systems. MATLAB's built-in ' lsqr' function can be used. Refer to the following MathWorks documentation for detailed information about 'lsqr' function: https://www.mathworks.com/help/matlab/ref/lsqr.html

## More Answers (0)

- quadratic program
- convex optimization
- unconstrained problem
- Optimization Toolbox

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Accepted Answer: Kartik Saxena. My algorithm contains solving a unconstrained quadratic problem. f (x) = 1/2*x'*A*x+b'*x, where A is a positive semidefinite matrix. Since the dimension of the matrix and vector is too large, the quadprog (using Interior point method in its iteration) runs too slow.